Some fixed point theorems on non-convex sets


  • M. Radhakrishnan University of Madras
  • S. Rajesh Indian Institute of Technology
  • Sushama Agrawal University of Madras



fixed points, nonexpansive mappings, T-regular set, k-uniform convex Banach spaces, Opial property


In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$


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Author Biographies

M. Radhakrishnan, University of Madras

Ramanujan Institute for Advanced Study in Mathematics

S. Rajesh, Indian Institute of Technology

Department of Mathematics

Sushama Agrawal, University of Madras

Ramanujan Institute for Advanced Study in Mathematics


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How to Cite

M. Radhakrishnan, S. Rajesh, and S. Agrawal, “Some fixed point theorems on non-convex sets”, Appl. Gen. Topol., vol. 18, no. 2, pp. 377–390, Oct. 2017.